The three-dimensional spatial arrangements of double helical DNA deformed along various supercoiled trajectories will be generated mathematically and then analyzed the detailed molecular level. The extent to which the regular linear duplex can be forced to bend and twist will then be monitored by semiempirical potential energy calculations. Bond lengths, valence angles, and torsion angles will be kept within normally prescribed limits, and steric and electrostatic interactions of nonbonded atoms and groups will be estimated with standard functions. Of particular interest will be the long-range effects associated with close contacts of sequentially distant chain residues. Long-range ionic effects will be examined using a newly modified Coulombia potential that reproduces the electrostatic interactions between charges on the surface of a dielectric cylinder immersed in salt water. The stabilities of various three-dimensional forms (e.g., toroidal, interwound, circular, etc.) will be compared and the detailed conformational variations of the standard double helical secondary structure examined. The relative contributions of bending and twisting to the total energy will be computed directly and compared with elastic models of supercoiling. The ability of the potential energy functions to account for macroscopic properties of the supercoils will be tested using established statistical mechanical procedures. Various secondary structural forms (e.g., A-, B-, Z-DNA) will be deformed along the superhelical trajectories in an attempt to understand the supercoil-induced conformational transitions of the DNA duplex.